Examples of Tree Diagram
Example 1:
You toss a fair coin and then roll a six-sided die. Represent this scenario using a tree diagram and find the probability of getting tails on the coin and an even number on the die.
Solution:
Create a tree diagram to show the possible outcomes of the coin toss and the dice roll. Assign probabilities to each branch. The probability of getting tails on the coin is , and the probability of getting heads is also . The probability of rolling an even number on the dice is , and the probability of rolling an odd number is .
Calculate the probability of the specific event (getting tails on the coin and an even number on the die) by multiplying the probabilities along the path,
P (Tails and Even) = P(Tails) × P(Even/Tails)
P (Tails and Even) =
P (Tails and Even) =
∴ The probability of getting tails on the coin and an even number on the die is .
Example 2:
Suppose there are two baskets, Basket A and Basket B. In Basket A, there are apples and oranges in the ratio of 3:7. Basket B contains bananas and grapes in the ratio of 1:1. If you first randomly choose a basket and then randomly select a fruit from the chosen basket, create a probability tree diagram representing this scenario. Find the probability of selecting an apple from Basket A and a grape from Basket B.
Solution:
Probability of Choosing Basket A =
Probability of Choosing an Apple from Basket A =
Probability of Choosing an Orange from Basket A =
Probability of Choosing Basket B =
Probability of Choosing a banana from Basket B =
Probability of Choosing a grape from Basket B =
The required probability of choosing an apple from basket A =
The required probability of choosing a grape from basket B =
Hence, the probability of selecting an apple from basket A and a grape from basket B =